OWL: Web Ontology Language

1
OWL Web Ontology Language
Slides are from Grigoris Antoniou, Frank van
Harmelen, A Semantic Web Primer
2
Limitations of RDF Schema

• Equivalence of classes
• Two classes, same concept - people use different
  words to represent the same thing. It would be
  very useful to be able to state "this class is
  equivalent to this second class".
• E.g. One person may create an ontology with a
  class called "Airplane". Another person may
  create an ontology with a class called "Plane".
  It would be useful to be able to indicate that
  the two classes are equivalent.
• Boolean combinations of classes
• Sometimes we wish to build new classes by
  combining other classes using union,
  intersection, and complement.
• E.g. Person is the union of the classes Male and
  Female persons.
• Disjointness of classes
• Sometimes we wish to say that classes are
  disjoint
• e.g. male and female are disjoint classes

3
Limitations of RDF Schema (continued)

• Cardinality constraints - oftentimes it is useful
  to indicate the allowable number of occurrences
  of a property
• E.g. We would like to be able to express that a
  River has only "one" officialLength property.
• E.g. We would like to be able to express that an
  Ocean has one maxDepth.
• E.g. a person has exactly two parents, a course
  is taught by at least one lecturer
• Special characteristics of properties
• Transitive property (like greater than)
• Unique property (like is mother of)
• A property is the inverse of another property
  (like eats and is eaten by)

4
RDF Schemas Building Block to More Expressive
Ontology Languages
OWL
OWL
RDF Schema
RDF Schema was designed to be extended. The
ontology languages all use RDF Schema's basic
notions of Class, Property, domain, and range.
5
What is OWL?

• OWL stands for Web Ontology Language
• OWL is built on top of RDF
• OWL is written in XML
• OWL is for processing information on the web
• OWL was designed to be interpreted by computers
• OWL was not designed for being read by people
• OWL is a web standard
• OWL has three sublanguages
• OWL Lite, DL, Full

The following slides are from Grigoris Antoniou,
Frank van Harmelen, A Semantic Web Primer
6
Tradeoff between Expressive Power and Efficient
Reasoning Support

• The richer the language is, the more inefficient
  the reasoning support becomes
• Sometimes it crosses the border of
  non-computability
• We need a compromise
• A language supported by reasonably efficient
  reasoners
• A language that can express large classes of
  ontologies and knowledge.

7
OWL Sublanguages

• OWL Lite
• Simple constraints and classification hierarchy
• OWL DL (includes OWL Lite)
• Maximal expressiveness while retaining
  computational completeness (all conclusions are
  computable)
• OWL Full (includes OWL DL)
• Maximal expressiveness
• Unlikely any reasoning software to support OWL
  Full.

OWL Full
OWL DL
OWL Lite
8
Reasoning About Knowledge in Ontology Languages

• Class membership
• If x is an instance of a class C, and C is a
  subclass of D, then we can infer that x is an
  instance of D.
• Subclass and Equivalence of classes
• If class A is equivalent to class B, and class B
  is equivalent to class C, then A is equivalent to
  C, too.
• Consistency
• X is an instance of classes A and B, but A and B
  are disjoint.
• This is an indication of an error in the
  ontology.

9
Uses for Reasoning

• Reasoning support is important for
• checking the consistency of the ontology and the
  knowledge
• checking for unintended relationships between
  classes
• automatically classifying instances in classes
• Checks like the preceding ones are valuable for
• designing large ontologies, where multiple
  authors are involved
• integrating and sharing ontologies from various
  sources

10
Reasoning support in OWL

• Semantics is a prerequisite for reasoning support
• Formal semantics and reasoning support are
  usually provided by
• mapping an ontology language to a known logical
  formalism
• using automated reasoners that already exist for
  those formalisms
• OWL is (partially) mapped on a description logic,
  and makes use of reasoners such as FaCT and RACER
  
• Description logics are a subset of predicate
  logic for which efficient reasoning support is
  possible

11
OWL Compatibility with RDF Schema

• All varieties of OWL use RDF for their syntax
• Instances are declared as in RDF, using RDF
  descriptions and typing information
• OWL constructors are specializations of their RDF
  counterparts

RdfsResources
RdfsProperty
RdfsClass
OwlObjectProperty
OwlDatatypeProperty
owlClass
OWL
RDF/RDFS
XML Schema
12
OWL Syntactic Varieties

• OWL builds on RDF and uses RDFs XML-based syntax
• Other syntactic forms for OWL have also been
  defined
• An abstract syntax, that is much more compact and
  readable than the XML languages
• A graphic syntax based on the conventions of UML

13
OWL XML/RDF Syntax Header

• ltrdfRDF
• xmlnsowl "http//www.w3.org/2002/07/owl"
• xmlnsrdf "http//www.w3.org/1999/02/22-rdf-synt
  ax-ns"
• xmlnsrdfs"http//www.w3.org/2000/01/rdf-schema
  "
• xmlnsxsd "http//www.w3.org/2001/XLMSchemagt

14
owlOntology

• An OWL ontology may start with a collection of
  assertions for housekeeping purposes using
  owlOntology element
• ltowlOntology rdfabout""gt
• ltrdfscommentgtAn example OWL ontology
  lt/rdfscommentgt
• ltowlpriorVersion
• rdfresource"http//www.mydomain.org/uni-ns-old
  "/gt
• ltowlimports
• rdfresource"http//www.mydomain.org/persons"/gt
  
• ltrdfslabelgtUniversity Ontologylt/rdfslabelgt
• lt/owlOntologygt
• owlimports is a transitive property

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Classes

• Classes are defined using owlClass
• owlClass is a subclass of rdfsClass
• ltowlClass rdfIDassociateProfessorgt
• ltrdfssubClassOf rdfresourceacademicStaffMemb
  er/gt
• lt/owlClassgt
• owlequivalentClass defines equivalence of
  classes
• ltowlClass rdfID"faculty"gt
• ltowlequivalentClass rdfresource"academ
  icStaffMember"/gt
• lt/owlClassgt
• Disjointness is defined using owldisjointWith
• ltowlClass rdfabout"associateProfessor"gt
• ltowldisjointWith rdfresource"professor"/gt
• ltowldisjointWith rdfresource"assistantProfe
  ssor"/gt
• lt/owlClassgt
• owlThing is the most general class, which
  contains everything
• owlNothing is the empty class

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Properties

• In OWL there are two kinds of properties
• Object properties, which relate objects to other
  objects
• E.g. is-TaughtBy, supervises
• ltowlObjectProperty rdfID"isTaughtBy"gt
• ltrdfsdomain rdfresource"course"/gt
• ltrdfsrange rdfresource "academicStaffMember"/
  gt
• ltrdfssubPropertyOf rdfresource"involves"/gt
• lt/owlObjectPropertygt
• Data type properties, which relate objects to
  datatype values
• E.g. phone, age, etc.
• ltowlDatatypeProperty rdfID"age"gt
• ltrdfsrange rdfresource "http//www.w3.org/20
  01/XLMSchemanonNegativeInteger"/gt
• lt/owlDatatypePropertygt

OWL
RDF/RDFS
XML Schema
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Relations to other properties

• Equivalent property
• ltowlObjectProperty rdfID"lecturesIn"gt
• ltowlequivalentProperty rdfresource"teaches"/
  gt
• lt/owlObjectPropertygt
• Inverse property
• ltowlObjectProperty rdfID"teaches"gt
• ltrdfsrange rdfresource"course"/gt
• ltrdfsdomain rdfresource "academicStaffMember"
  /gt
• ltowlinverseOf rdfresource"isTaughtBy"/gt
• lt/owlObjectPropertygt

18
Property restriction

• Value constraints put constrains on the range of
  the property when applied to this particular
  class description.
• owlallValuesFrom specifies universal
  quantification
• owlhasValue specifies a specific value
• owlsomeValuesFrom specifies existential
  quantification
• Cardinality constraints the number of value a
  property can take.

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owlallValuesFrom

• Define the class of persons whose parents are
  both physicians.
• ltowlRestrictiongt
• ltowlonProperty rdfresource"hasParent" /gt
  
• ltowlallValuesFrom rdfresource"Physician"
  /gt
• lt/owlRestrictiongt
• x (x, y) ? hasParent implies y ? Physician
• Example
• Suppose David hasParent Bill who is a Physician,
  and David hasParent Rose who is a Phycisian
• Conclusion David belongs to the class defined
  above.
• Semantics
• restriction(p allValuesFrom(r))
• x (x,y) ? p implies y ? r

20
allValuesFrom

• FirstYearCourse is a course that must be taught
  by professors
• ltowlClass rdfabout"firstYearCourse"gt
• ltrdfssubClassOfgt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"isTaughtBy"/gt
• ltowlallValuesFrom rdfresource"Professor"/
  gt
• lt/owlRestrictiongt
• lt/rdfssubClassOfgt
• lt/owlClassgt
• x (x,y) ?isTaughtBy implies y ? Professor

21
owlsomeValuesFrom

• Define the class of persons who has at least one
  physician parent.
• ltowlRestrictiongt
• ltowlonProperty rdfresource"hasParent" /gt
  
• ltowlsomeValuesFrom rdfresource"Physician"
  /gt
• lt/owlRestrictiongt
• x ? (x, y) ? hasParent ? y ? Physician
• Semantics
• restriction(p someValuesFrom(e))
• x ? (x,y) ? p ? y ? e

22
someValuesFrom

• AcademicStaff must teach at least one under
  course.
• ltowlClass rdfabout"academicStaffMember"gt
• ltrdfssubClassOfgt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"teaches"/gt
• ltowlsomeValuesFrom rdfresource"undergraduate
  Course"/gt
• lt/owlRestrictiongt
• lt/rdfssubClassOfgt
• lt/owlClassgt
• x ? (x, y) ? Teaches ? y ? undergraduateCourse
  
• Example
• Suppose David Teaches 440, and David Teaches 569
• Question Is David an Academic Staff?

23
owlhasValue

• ltowlClass rdfabout"mathCourse"gt
• ltrdfssubClassOfgt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"isTaughtBy
  "/gt
• ltowlhasValue rdfresource "949352"/gt
• lt/owlRestrictiongt
• lt/rdfssubClassOfgt
• lt/owlClassgt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"hasParent" /gt
  
• ltowlhasValue rdfresource"Bill" /gt
• lt/owlRestrictiongt
• restriction(p value(i)), for i an individual ID
• x (x, i) ? p

24
Cardinality restrictions

• We can specify minimum and maximum number using
  owlminCardinality and owlmaxCardinality
• It is possible to specify a precise number by
  using the same minimum and maximum number
• For convenience, OWL offers also owlcardinality
• E.g. Every course is taught by at least someone
• ltowlClass rdfabout"course"gt
• ltrdfssubClassOfgt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"isTaughtBy"/
  gt
• ltowlminCardinality rdfdatatype"xsdnonN
  egativeInteger"gt
• 1
• lt/owlminCardinalitygt
• lt/owlRestrictiongt
• lt/rdfssubClassOfgt
• lt/owlClassgt

25
Special properties

• owlTransitiveProperty (transitive property)
• E.g. has better grade than, is ancestor of
• owlSymmetricProperty (symmetry)
• E.g. has same grade as, is sibling of
• owlFunctionalProperty defines a property that
  has at most one value for each object
• E.g. age, height, directSupervisor
• owlInverseFunctionalProperty defines a property
  for which two different objects cannot have the
  same value
• ltowlObjectProperty rdfID"hasSameGradeAs"gt
• ltrdftype rdfresource"owlTransitiveProperty"
  /gt
• ltrdftype rdfresource"owlSymmetricProperty"/
  gt
• ltrdfsdomain rdfresource"student"/gt
• ltrdfsrange rdfresource"student"/gt
• lt/owlObjectPropertygt

26
Boolean Combinations complementOf

• We can combine classes using Boolean operations
  (union, intersection, complement)
• ltowlClass rdfabout"course"gt
• ltrdfssubClassOfgt
• ltowlRestrictiongt
• ltowlcomplementOf rdfresource"staffMembe
  r"/gt
• lt/owlRestrictiongt
• lt/rdfssubClassOfgt
• lt/owlClassgt

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Boolean Combinations unionOf

• ltowlClass rdfID"peopleAtUni"gt
• ltowlunionOf rdfparseType"Collection"gt
• ltowlClass rdfabout"staffMember"/gt
• ltowlClass rdfabout"student"/gt
• lt/owlunionOfgt
• lt/owlClassgt
• The new class is not a subclass of the union, but
  rather equal to the union
• We have stated an equivalence of classes

28
Boolean Combinations intersectionOf

• ltowlClass rdfID"facultyInCS"gt
• ltowlintersectionOf rdfparseType"Collection"gt
• ltowlClass rdfabout"faculty"/gt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"belongsTo"/gt
  
• ltowlhasValue rdfresource
  "CSDepartment"/gt
• lt/owlRestrictiongt
• lt/owlintersectionOfgt
• lt/owlClassgt
• Exercise describe the class of faculty who have
  joint appointment in CS and ECE.

29
Nesting of Boolean Operators

• Administrative staff staff members who are
  neither faculty nor technical support staff.
• ltowlClass rdfID"adminStaff"gt
• ltowlintersectionOf rdfparseType"Collection"gt
• ltowlClass rdfabout"staffMember"/gt
• ltowlcomplementOfgt
• ltowlunionOf rdfparseType"Collection"gt
• ltowlClass rdfabout"faculty"/gt
• ltowlClass rdfabout
  "techSupportStaff"/gt
• lt/owlunionOfgt
• lt/owlcomplementOfgt
• lt/owlintersectionOfgt
• lt/owlClassgt

staff
admin
tech
faculty
30
Enumerations with owloneOf

• ltowloneOf rdfparseType"Collection"gt
• ltowlThing rdfabout"Monday"/gt
• ltowlThing rdfabout"Tuesday"/gt
• ltowlThing rdfabout"Wednesday"/gt
• ltowlThing rdfabout"Thursday"/gt
• ltowlThing rdfabout"Friday"/gt
• ltowlThing rdfabout"Saturday"/gt
• ltowlThing rdfabout"Sunday"/gt
• lt/owloneOfgt
• Now we have talked about three ways to describe a
  class
• Enumeration
• Set operation
• Property restriction

31
Declaring instances

• Instances of classes are declared as in RDF
• ltrdfDescription rdfID"949352"gt
• ltrdftype rdfresource "academicStaffMember"/gt
• lt/rdfDescriptiongt
• Or alternatively, we can have the following
  simplified notation
• ltacademicStaffMember rdfID"949352"gt
• lt/academicStaffMembergt

32
No Unique-Names Assumption

• OWL does not adopt the unique-names assumption of
  database systems
• If two instances have different names or IDs, it
  does not imply that they are different
  individuals
• Suppose we state that each course is taught by at
  most one staff member, and that a given course
  is taught by two staff members
• An OWL reasoner does not flag an error
• Instead it infers that the two resources are
  equal.

33
Distinct Objects

• To ensure that different individuals are indeed
  recognized as such, we must explicitly assert
  their inequality
• ltlecturer rdfabout"949318"gt
• ltowldifferentFrom rdfresource"949352"/gt
• lt/lecturergt
• OWL provides a shorthand notation to assert the
  pairwise inequality of all individuals in a given
  list
• ltowlallDifferentgt
• ltowldistinctMembers rdfparseType"Collection"gt
• ltlecturer rdfabout"949318"/gt
• ltlecturer rdfabout"949352"/gt
• ltlecturer rdfabout"949111"/gt
• lt/owldistinctMembersgt
• lt/owlallDifferentgt

34
Data Types in OWL

• XML Schema provides a mechanism to construct
  user-defined data types
• E.g., the data type of adultAge includes all
  integers greater than 18
• Such derived data types cannot be used in OWL
• The OWL reference document lists all the XML
  Schema data types that can be used
• These include the most frequently used types such
  as string, integer, Boolean, time, and date.

35
An African Wildlife Ontology Class Hierarchy
Animal
plant
carnivore
herbivore
tree
giraffe
lion
36
An African Wildlife Ontology Properties

• ltowlTransitiveProperty rdfID"is-part-of"/gt
• ltowlObjectProperty rdfID"eats"gt
• ltrdfsdomain rdfresource"animal"/gt
• lt/owlObjectPropertygt
• ltowlObjectProperty rdfID"eaten-by"gt
• ltowlinverseOf rdfresource"eats"/gt
• lt/owlObjectPropertygt

37
An African Wildlife Ontology Plants and Trees

• ltowlClass rdfIDanimal/gt
• ltowlClass rdfID"plant"gt
• ltrdfscommentgtPlants are disjoint from animals.
• lt/rdfscommentgt
• ltowldisjointWith"animal"/gt
• lt/owlClassgt
• ltowlClass rdfID"tree"gt
• ltrdfscommentgtTrees are a type of plant.
• lt/rdfscommentgt
• ltrdfssubClassOf rdfresource"plant"/gt
• lt/owlClassgt

38
An African Wildlife Ontology Branches

• ltowlClass rdfID"branch"gt
• ltrdfscommentgtBranches are parts of trees.
  lt/rdfscommentgt
• ltrdfssubClassOfgt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"is-part-of"/gt
• ltowlallValuesFrom rdfresource"tree"/gt
• lt/owlRestrictiongt
• lt/rdfssubClassOfgt
• lt/owlClassgt

39
An African Wildlife Ontology Leaves

• ltowlClass rdfID"leaf"gt
• ltrdfscommentgtLeaves are parts of branches.
  lt/rdfscommentgt
• ltrdfssubClassOfgt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"is-part-of"/gt
• ltowlallValuesFrom rdfresource"branch"/gt
• lt/owlRestrictiongt
• lt/rdfssubClassOfgt
• lt/owlClassgt

40
An African Wildlife Ontology Carnivores

• ltowlClass rdfID"carnivore"gt
• ltrdfscommentgt
• Carnivores are exactly those animals
  that eat also animals.
• lt/rdfscommentgt
• ltowlintersectionOf rdfparsetype"Collection"gt
• ltowlClass rdfabout"animal"/gt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"eats"/gt
• ltowlsomeValuesFrom rdfresource"animal"/gt
• lt/owlRestrictiongt
• lt/owlintersectionOfgt
• lt/owlClassgt

41
An African Wildlife Ontology Herbivores

• ltowlClass rdfID"herbivore"gt
• ltrdfscommentgt Herbivores are exactly those
  animals
• that eat only plants or parts of plants.
• ltowlintersectionOf rdfparseTypeCollectiongt
• ltowlClass rdfaboutanimal/gt
• ltowlRestrictiongt
• ltowlonProperty rdfresourceeats/gt
• ltowlallValuesFromgt
• ltowlClassgt
• ltowlunionOf rdfparseTypeCollecti
  ongt
• ltowlClass rdfresourceplant/gt
• ltowlRestrictiongt
• ltowlonProperty
  rdfresourceis_part_of/gt
• ltowlallValuesFrom
  rdfresourceplant/gt
• lt/owlRestrictiongt
• lt/owlunionOfgt
• lt/classgt
• lt/owlallValuesFromgt
• lt/owlRestrcitiongt

42
An African Wildlife Ontology Giraffes

• ltowlClass rdfID"giraffe"gt
• ltrdfscommentgtGiraffes are herbivores, and they
  eat only leaves.
• lt/rdfscommentgt
• ltrdfssubClassOf rdftype"herbivore"/gt
• ltrdfssubClassOfgt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"eats"/gt
• ltowlallValuesFrom rdfresource"leaf"/gt
  
• lt/owlRestrictiongt
• lt/rdfssubClassOfgt
• lt/owlClassgt

43
An African Wildlife Ontology Lions

• ltowlClass rdfID"lion"gt
• ltrdfscommentgtLions are animals (carnivores)
  that eat only herbivores.
• lt/rdfscommentgt
• ltrdfssubClassOf rdftype"carnivore"/gt
• ltrdfssubClassOfgt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"eats"/gt
• ltowlallValuesFrom rdfresource"herbivore"/gt
• lt/owlRestrictiongt
• lt/rdfssubClassOfgt
• lt/owlClassgt

44
An African Wildlife Ontology Tasty Plants

• ltowlClass rdfID"tasty-plant"gt
• ltrdfscommentgtPlants eaten both by herbivores
  and carnivores lt/rdfscommentgt
• ltrdfssubClassOf rdfresourceplant/gt
• ltrdfssubClassOfgt
• ltowlRestrictiongt
• ltowlonProperty rdfresourceeaten_by/gt
• ltowlsomeValuesFromgt ltowlClass
  rdfaboutherbivore/gt
• lt/owlsomeValuefromgt
  
• lt/owlRestrictiongt
• lt/rdfssubClassOfgt
• ltrdfssubClassOfgt
• ltowlRestrictiongt
• ltowlonProperty rdfresourceeaten_by/gt
• ltowlsomeValuesFromgt ltowlClass
  rdfaboutcarnivore/gt
• lt/owlsomeValuefromgt
• lt/owlRestrictiongt
• lt/rdfsSublassOfgt
• lt/owlClassgt

45
Closed World Assumption

• OWL currently adopts the open-world assumption
• A statement cannot be assumed true on the basis
  of a failure to prove it
• On the huge and only partially knowable WWW, this
  is a correct assumption
• Closed-world assumption a statement is true when
  its negation cannot be proved
• tied to the notion of defaults, leads to
  nonmonotonic behaviour

46
Summary

• OWL is the proposed standard for Web ontologies
• OWL builds upon RDF and RDF Schema
• (XML-based) RDF syntax is used
• Instances are defined using RDF descriptions
• Most RDFS modeling primitives are used
• Formal semantics and reasoning support is
  provided through the mapping of OWL to logics
• Predicate logic and especially description logics
  have been used for this purpose
• While OWL is sufficiently rich to be used in
  practice, extensions are in the making
• They will provide further logical features,
  including rules

47
Look back at the definition for ontology

• An ontology is a formal, explicit specification
  of a shared conceptualization - Gruber
• Conceptualization refers to an abstract model of
  phenomena.
• Explicit means that the type of concepts used,
  and the constraints on their use are explicitly
  defined.
• Formal refers to the fact that the ontology
  should be machine readable.
• Shared reflects that ontology should capture
  consensual knowledge accepted by the communities.